Biofuel Cells. Группа авторов

making it easier to oxidize. Experimentally, this can be observed as a shift in its formal redox potential

in the negative direction. The opposite effect is observed for electron withdrawing functional groups.

      Organic molecules have also been used as mediators. As pointed out earlier, methylene blue (a phenothiazine) was one of the first mediators employed, although it is no longer common in enzymatic biofuel cells. Other phenothiazines have been used as well, including methylene green [42], toluidine blue [131] and thionine [6]). Pyrroloquinoline quinone (PQQ), a cofactor of several enzymes, including glucose dehydrogenase has also been used as a mediator for enzymes that do not naturally employ it. Glucose oxidase and lactate dehydrogenase, for example, have been shown to couple with PQQ-containing self-assembled monolayers to shuttle electrons to Au surfaces [132]. It is believed that the fact that the mediator reaction is a 2-electron one, similarly to the enzymatic reaction, can help simplify the electron transfer process [133].

Ramanavicius’ group has studied the use of phenanthroline derivatives (not coordinated to a metal) as mediators for glucose oxidase. They reported that amine electron-donating substituents performed more favorably than nitro electron-withdrawing groups [55]. They note this is in contrast with the above-described results for ligands in metal complexes and cannot be rationalized purely in terms of the effects of electron density on the redox potential. As well, they successfully used a dione phenanthroline derivative to mediate the anode reaction in a GOx-based biofuel cell [13].

In order for a molecule to work as a mediator, its formal redox potential

must have the appropriate value relative to the one for the enzyme cofactor

. At the anode,

must be higher than

so that the mediator is capable of reoxidizing the reduced enzyme back to its active state. Conversely,

must be lower than

at the cathode (Figure 1.10). It is important to realize that these requirements necessary introduce thermodynamic potential losses, therefore decreasing the open circuit voltage of the cell. Therefore, a balance must be sought to have a large enough separation between

and

to drive the mediation reaction thermodynamically but to minimize the open circuit potential losses. In any case, the potential losses are compensated for with the increased kinetics caused by the presence of the mediator.

      Depending on the enzyme employed, the reaction between the enzyme and the mediator might be in competition with the one between the enzyme and its natural acceptor. Such is the case of GOx, in which oxygen competes for the electrons with the mediator. In these cases, the concentration of the mediator must be high enough to favor a predominant enzymemediator reaction. On the other hand, when using glucose dehydrogenase for example, the enzyme activity is not dependent on oxygen and therefore no competition exists [5].

Figure 1.10 Schematic of the i − E curves for mediated and non-mediated electrodes in a fuel cell. The shaded areas represent twice the power of a fuel cell working at a given current value.

Mediator molecules are usually immobilized on the electrode surface along with the enzyme and significant theory has been developed for these systems. Particularly, Barlett and Pratt and have classified the behavior of mediated electrodes in a series of “cases” according to the relative amounts of enzyme, substrate and mediator, as well as the relative rates of charge transport, charge transfer and reagent and product diffusion [134]. This is important because, since the observed current is the result of many sequential steps, different experimental conditions can result in a variety of limiting steps. The understanding of the effect of these parameters on the rates can help make sense of the observed experimental dependencies and design a system accordingly.

      Early strategies of mediator immobilization included the use of thiol self-assembled monolayers (SAMs) on Au substrates. The initial SAM would be modified with a mediator molecule that contained the enzyme cofactor at its distal end. Addition of the apoenzymes would result in reconstitution and enzymatic activity [132, 133]. Monolayer-based electrode modification is limited by the available surface area of the electrode. Therefore, surface roughening is employed to maximize the immobilization area.

      A different alternative to increase the current per unit of electrode area is the incorporation of the mediator in the chains of a polymer, thus creating the so-called redox polymers [135]. Poly(vinylimidazoles)s, poly (vinylpyridine)s, poly(allylamine)s and poly(ethyleneimine)s have been covalently modified with mediators and cross-linked along with enzymes to form hydrogels. Poly(vinylimidazoles)s, poly(allylamine)s and poly(ethyleneimine)s have primary and/or secondary amine groups that, as discussed in Section 1.3.1, can react with some of the cross-linkers. Poly(-vinylpyridine)s, on the other hand, possess only tertiary amines that are less reactive with the cross-linkers. Redox polymer hydrogels concentrate a large number of mediator molecules close to the surface of the electrode, thus producing high currents. When analyzed via cyclic voltammetry in the absence of enzyme and/or substrate, these systems typically show a diffusion-like behavior. This can be explained though the theory of electron hopping developed in the 60s and 70s by Dahms [136] and Ruff and Friedrich [137]. According to this model, neighboring redox moieties undergo a self-exchange reaction. The flow of electrons in the three-dimensional network of mediator molecules can be described by the same Fick laws that describe diffusion of dissolved substances. Therefore, the rate at which electrons are exchanged in the redox polymer hydrogel is represented by an apparent electron diffusion coefficient (D_e). Consequently, a diffusion-like layer of thickness (D_et)^1/2—where t is time—can be calculated.

If the thickness of this diffusion-like layer is much smaller than the hydrogel thickness, the voltammograms represent a process limited by semi-infinite diffusion [47]. However, if enough time is given so that (D_et)^1/2 grows larger than the film thickness (using slow potential scan rates), thin layer behavior is expected. Of course, this approach is applicable not only to redox polymers, but also to electroactive molecules immobilized by any other method, like ion exchange for example [138].

      In early works, poly(allylamine) was modified with [Fe(CN)₅]^3−/2−, [Ru(HN₃)₅]^2+/3+ and [Os(bpy)₂Cl(PyCH₂)] and proven to communicate with immobilized GOx [47, 48]. Poly(vinylpyridine) has as well been modified with [Os(bpy)₂Cl] and cross-linked with PEGDGE in a multienzyme mixture that includes glucose oxidase in an interesting study that compares multiple immobilization approaches [39]. Poly(vinylimidazole) has been modified with [Os(bpy)₂] and compared the performance when cross-linking the hydrogel with GA and PEGDGE. While GA seems to produce higher currents, it presents lower stability than the PEGDGE counterparts [56].

      Recent years have seen an increase in the use of poly(ethyleneimine)-based redox polymers as components of enzyme/mediator hydrogels. In particular, linear poly(ethyleneimine) (LPEI) has been attracting considerable attention because it presents less toxicity than branched PEIs [139], which is desirable for implantable electrodes. LPEI has been commonly modified with ferrocene (Fc-C₃-LPEI) [51, 140–145] and its dimethylated (FcMe₂-C₃-LPEI) [51, 54, 63, 65, 146–148] and tetramethylated (FcMe₄-C₃-LPEI)